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Remarks on Units of Skew Monoidal Categories

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Abstract

This article shows that the axioms of a skew monoidal category are independent and that its unit is unique up to a unique isomorphism together with an analogue of this result for monoidal functors between skew monoidal categories. It is also noted that these results carry over to skew monoidales before some benefits of certain extra structure on the unit maps of a skew monoidal category are discussed.

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References

  1. Altenkirch, T., Chapman, J., Uustalu, T.: Monads need not be endofunctors. Lect. Notes in Comput. Sci., vol. 6014. Springer (2010)

  2. Andrianopoulos, J: Remarks on units of skew monoidal categories. arXiv:1505.02048 (2015)

  3. Joyce, W.P.: Natural associativity without the pentagon condition. arXiv:0109088v2 (2003)

  4. Max Kelly, G.: On MacLane’s conditions for coherence of natural associativities, commutativities, etc. J. Algebra 1, 397–402 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kock, J.: Elementary remarks on units in monoidal categories. Math. Proc. Cambridge Philosoph. Soc. 144(1), 53–76 (2008)

    MathSciNet  MATH  Google Scholar 

  6. Lack, S., Street, R.: Skew monoidales, skew warpings and quantum categories. Theory Appl. Categ. 26, 385–402 (2012)

    MathSciNet  MATH  Google Scholar 

  7. Mac Lane, S.: Natural associativity and commutativity. Rice Univ. Stud. 49(4), 28–46 (1963)

    MathSciNet  MATH  Google Scholar 

  8. Rivano, N.S.: Catégories Tannakiennes. LNM, vol. 265. Springer-Verlag (1972)

  9. Szlachányi, K.: Skew-monoidal categories and bialgebroids. Adv. Math. 231 (3-4), 1694–1730 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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  1. Macquarie University Faculty of Science, Sydney, Australia

    Jim Andrianopoulos

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  1. Jim Andrianopoulos
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Correspondence to Jim Andrianopoulos.

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Andrianopoulos, J. Remarks on Units of Skew Monoidal Categories. Appl Categor Struct 25, 863–873 (2017). https://doi.org/10.1007/s10485-016-9468-5

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  • DOI: https://doi.org/10.1007/s10485-016-9468-5

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